Chapter 9 : Viscous Incompressible Flows
Lecture 29 : Laminar Boundary Layers


Example

The above engineering system shows a series of thin parallel plates aligned with the intake flows. The plate spacing is h and the plate length is L.

Assume that the flow is incompressible. Derive expression for the pressure drop pin-pout between inflow and outflow streams for the high velocity flow where a boundary layer develops on each surface independent of adjacent plates.

Solution.

The drag force on each plate is

Now choosing one channel as control volume


or,     

or,          independent of the width of the plate

 

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